This invention relates to a cooling system for use with a combustion engine and comprising a radiator having a number of cooling medium pipes which communicate on the one side with an inlet and on the other side with an outlet for cooling medium. A plurality of metal parts such as strips or gauze are connected to said pipes on which they extend in the transverse direction and with which they are in heat-conductive contact. The said pipes are arranged mainly in one plane. Cooling systems comprising a radiator of the kind set forth are known and have the drawback that they are rather bulky which is inconvenient when building such radiators into cars; also the material costs are substantial due to their large weight.